New graphics card shutting down computer?

Christmas day I installed a Sapphire HD 3870 DDR4 512 gpu. I have been getting intermittent shut downs since. No artifacts or tearing, it just goes into recover mode. It is more likely to happen in gpu intensive games but will even happen while searching the net. According to CCC my temps are less than 50c under full load so I don't think it is over heating. The stock clocks are 776/1126 if I leave them at this setting I am far less likely to shut down, but it may still happen in graphic intensive applications. If I let CCC overclock in Autotune it clocks somewhere around 781/1131 (not much of an overclock at all) and will shut down VERY soon and often! When I test the overclock using CCC overclock testing it is random whether or not the over clock will pass, even if it is an autotune overclock. I am using 8.12 driver. Here are my system specs.

System Requirement:
PCI Express based PC is required with one X16 lane graphic slot available on the motherboard.
1GB or greater system memory for better performance.
450Watt or greater power supply with 75 Watt 6-pin PCI Express power connector recommended.
For ATI CrossfireX: 550 watt power supply or greater with two 6-pin connectors.
Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products.

I am planning a power supply upgrade as I thought mine may be to weak. Although the Dell 375w power supply does have 30a on the 12v. rail and the 75w connector. I have heard and read a lot of contradictory information about Dells 375w power supply, from "it is a very high quality 375w power supply with lots of amps in the right place because they offered the 8800gt card with this same power supply",.... to "it is junk and would not run any of the gpu cards offered". I am going to upgrade power supplies but to be honest I don't think that is my problem. The shut down is so random, no real rhyme or reason? I would think that a power supply problem would always show up under heavy loads, not while net surfing.